I don't think that it is correct to expect that a mathematical object has a
Head. Mathematica only gives us various representations of objects and
different representations have different Heads. Thus
3 + 4 I, ComplexPolar[5, ArcTan[4/3]] (in Presentations), 5 E^(I
ArcTan[4/3]), Complex[3,4]
all represent the same mathematical object but all have different Heads.
(Plus, ComplexPolar, Times, Complex).
What might be confusing is that Complex is a NUMBER and not a symbolic
expression. WRI could improve the Help for Complex by changing the first
note to:
"You can enter a complex number in the form x + I y, where x and y are
Integer, Real, Rational or Complex numbers."
"Expressions such as Complex[a,b] with Symbols are not meaningful and are
left unevaluated. Symbolic complex expressions contain Complex numbers only
as subparts."
And then, among the first examples, they might show:
"Complex expressions may contain Complex numbers as subparts and can be
manipulated with routines such as Conjugate and ComplexExpand."
x + I y
% // FullForm
ComplexExpand[Conjugate[%]]
% // FullForm
x + I y
Plus[x,Times[Complex[0,1],y]]
x - I y
Plus[x,Times[Complex[0,-1],y]]
Very few users would use Complex numbers in isolation without combining them
in symbolic expressions. So why not stand users up and point them in the
right direction instead of just saying that the Help is 'formally correct'?
For those who use Help, of course.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/
From: Richard Fateman [mailto:fateman at cs.berkeley.edu]
[SNIP]
Are you describing Mathematica here? It seems to me that it is an
exception that Head[a+b*I] is Plus, but Head[3+4I] is Complex.
[SNIP]
You assume that people read the documentation. This is provably false.
RJF